# [Maxima] eigenvalue, eigenvector

ahmet alper parker aaparker at gmail.com
Wed May 28 13:29:40 CDT 2008

```I missed a syntax, sorry! The red one below... Also I have calculated the
correct values by eigenvector function as (M^1.K) the matrix for eigens.

On Wed, May 28, 2008 at 9:24 PM, ahmet alper parker <aaparker at gmail.com>
wrote:

>
>
> On Wed, May 28, 2008 at 9:24 PM, ahmet alper parker <aaparker at gmail.com>
> wrote:
>
>> I am trying to do a modal analysis with K the stiffness matrix and M the
>> mass matrix and trying to find K*lamda=w^2*M*lamda. Looking at the matlabs
>> help files, I discovered that I can use (M^-1.K) to calculate the
>> eigenvalues and eigenvectors with the standard functions. But when I tried
>> to find (according to my knowledge) the eigenvectors, The only method I know
>> did not worked for the eigenvectors.
>> For example
>> writing w^2 in the equation and solving for lamda, the lamda is a vector
>> and as far as I know I have to enter 1 to at least one of them, since they
>> are not independent. Then I solve the others from the matrix equation.
>>
>>
>> K:matrix([(12*E*I)/L^3,0,0],[0,(3.555555555555555*E*I)/L^3,-(3.555555555555555*E*I)/L^3],[0,-(3.555555555555555*E*I)/L^3,(7.111111111111111*E*I)/L^3]);
>> M:matrix([(m*L)/2,0,0],[0,(5*m*L)/4,0],[0,0,(3*m*L)/2]);
>> J:K-w^2*M;
>> solve([determinant(J)=0;], [w]);
>>
>> I got eigenvalues correctly.
>> subst((8*sqrt(sqrt(34)+8)*sqrt((E*I)/m))/(3*sqrt(15)*L^2), w, J);
>> t:%;
>>
>

> linsolve([t[1,1]*lamda1+t[1,2]*lamda2+t[1,3]*lamda3=0,
>> t[2,1]*lamda1+t[2,2]*lamda2
>>  +t[2,3]*lamda3=0, t[3,1]*lamda1+t[3,2]*lamda2+t[3,3]*lamda3=0],
>> [lamda1,lamda2,lamda3]);
>
>

>
>> I get:
>> [lamda1=0,lamda2=(48*%r1^2-2046*%r1)/(325*%r1+410),lamda3=%r1];
>>
>> when I try lamda1=0 and
>> algsys([t[2,2]*lamda2+t[2,3]*lamda3=0, t[3,2]*lamda2+t[3,3]*lamda3=0],
>> [lamda2,lamda3]);
>>
>> I get:
>>
>> [[lamda2=%r2,lamda3=-((sqrt(34)+2)*%r2)/6]];
>>
>> I get different lamdas...
>> As you can see, the first set of lamdas are not %r1 proportional so when I
>> give %r1 different values, I will get non proportional results...
>> In the second, however, they are proportional to %r2,
>>
>> Which one is correct? (Or both wrong?)
>>
>> Regards
>> A.A.Parker
>>
>>
>>
>>
>>
>>
>>
>> On Wed, May 28, 2008 at 8:39 PM, Raymond Toy (RT/EUS) <
>> raymond.toy at ericsson.com> wrote:
>>
>>> ahmet alper parker wrote:
>>>
>>>> Dear all,
>>>> I have a K matrix as
>>>>
>>>> K:matrix([(12*E*I)/L^3,0,0],[0,(3.555555555555555*E*I)/L^3,-(3.555555555555555*E*I)/L^3],[0,-(3.555555555555555*E*I)/L^3,(7.111111111111111*E*I)/L^3]);
>>>> and an M matrix as
>>>> M:matrix([(m*L)/2,0,0],[0,(5*m*L)/4,0],[0,0,(3*m*L)/2]);
>>>> and I am trying to solve
>>>> (K-w^2*M)*f=0 eigenvalue problem. (Solving for w eigenvalue and f
>>>> eigenvector)
>>>> When making manually by equating the determinant to zero and solving for
>>>> w, I get the w correct. But when I tried to solve for f, I got different
>>>> answers depending on the method I choose,
>>>> First solving as a linear equation with 3 equations I get one set of
>>>> eigenvectors,
>>>> Second, first eigenvector's first term is zero. I get the first equation
>>>> out of the system and solved for the rest two equations, I get different
>>>> eigenvectors,
>>>> Also, they are not proportional, I mean taking one of the eigenvector
>>>> values as unity makes the other some value, however taking the other as unit
>>>> makes the other another different value, in which I cannot properly unitize
>>>> them. I mean, if I take the second value of the eigenvector 1 , the other
>>>> (third) is say 0.5 however, if I take the third as 1 it does not make the
>>>> second 2.
>>>>
>>>
>>> I'm thoroughly confused by what you're saying here.  Can you show what
>>> you're actually doing?
>>>
>>> Ray
>>>
>>
>>
>
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